Chapter5 1 5. Quantum Walks in Quasi-Periodic Photonics Lattices

Abstract We present construction rules for a new class of quasiperiodic photonics lattices (QPL) to realize localized quantum walks (LQWs) deterministically. The new quasiperiodic structures are constructed symmetrically with Fibonacci, Thue-Morse, and other quasiperiodic sequences. Our construction rules allow us to build the symmetrical quasiperiodic photonics lattices. As a result, LQWs with symmetrical probability distributions can be realized in these QPLs. Furthermore, the proposed QPLs are composed with different waveguides providing both on- and off-diagonal deterministic disorders. We show LQWs in the proposed QPLs are highly programmable and controllable.